1. A Guide to Mass transfer equations
By: Ahmed Al-Marjibi

2. X
This program is targeted toward junior chemical engineering student and students taking a heat and mass transfer class.

3. X
Choose contactor type
Tank
Tubular

4. Choose one of the 3 main tank type mass contactorsX
Choose one of the 3 main tank type mass contactors
Batch
Semi-Batch
Continuous
(Choose One)

5. Tank type Continuous ContactorX
Tank type Continuous Contactor
(Choose one)
phase balance
𝑪 𝑨 𝑰
𝑪 𝑨 𝑰𝑰
𝑽 𝑰𝑰
Back to tank type list

6. Tank type Continuous Contactor: Phase balanceX
Tank type Continuous Contactor: Phase balance
0= 𝑞 𝐼 𝐶 𝐴𝐹 𝐼 − 𝐶 𝐴 𝐼 − 𝑘 𝑚 𝑎( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
0= 𝑞 𝐼𝐼 𝐶 𝐴𝐹 𝐼𝐼 − 𝐶 𝐴 𝐼𝐼 + 𝑘 𝑚 𝑎( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
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7. Tank type Continuous Contactor: 𝐶 𝐴 𝐼X
Tank type Continuous Contactor: 𝐶 𝐴 𝐼
𝐶 𝐴 𝐼 =𝑀 𝐶 𝐴𝐹 𝐼 +𝜆 𝐶 𝐴𝐹 𝐼𝐼 𝜆+𝑀
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8. Tank type Continuous Contactor: 𝐶 𝐴 𝐼𝐼X
Tank type Continuous Contactor: 𝐶 𝐴 𝐼𝐼
𝐶 𝐴 𝐼𝐼 = 𝐶 𝐴𝐹 𝐼 +𝜆 𝐶 𝐴𝐹 𝐼𝐼 𝜆+𝑀
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9. Tank type Continuous Contactor: 𝑉 𝐼𝐼X
Tank type Continuous Contactor: 𝑉 𝐼𝐼
𝑉 𝐼𝐼 = 𝑎𝑑 6
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10. Tank type semi-Batch ContactorX
Tank type semi-Batch Contactor
(Choose one)
Overall phase balance
Phase I Energy balance
Phase II Energy balance
Back to tank type list

11. Tank type semi-Batch Contactor: overall phase balanceX
Tank type semi-Batch Contactor: overall phase balance
𝑑 𝑑𝑡 𝐶 𝐴 𝐼 𝑉 𝐼 + 𝑑 𝑑𝑡 𝐶 𝐴 𝐼𝐼 𝑉 𝐼𝐼 = 𝑞 𝐼𝐼 ( 𝐶 𝐴𝐹 𝐼𝐼 − 𝐶 𝐴 𝐼𝐼 )
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12. Tank type semi-Batch Contactor: Phase I energy balanceX
Tank type semi-Batch Contactor: Phase I energy balance
𝑑 𝑑𝑡 𝐶 𝐴 𝐼 𝑉 𝐼 =− 𝑘 𝑚 𝑎 𝐶 𝐴 𝐼 −𝑓( 𝐶 𝐴 𝐼𝐼 )
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13. Tank type semi-Batch Contactor: Phase II energy balanceX
Tank type semi-Batch Contactor: Phase II energy balance
𝑑 𝑑𝑡 𝐶 𝐴 𝐼𝐼 𝑉 𝐼𝐼 = 𝑘 𝑚 𝑎 𝐶 𝐴 𝐼 −𝑓( 𝐶 𝐴 𝐼𝐼 ) + 𝑞 𝐼𝐼 ( 𝐶 𝐴𝐹 𝐼𝐼 − 𝐶 𝐴 𝐼𝐼 )
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14. Tank type Batch ContactorX
Tank type Batch Contactor
(Choose a variable)
phase balance
𝑪 𝑨 𝑰
𝑪 𝑨,𝒆𝒒 𝑰𝑰
𝑽 𝑰𝑰
Back to tank type list

15. Tank type Batch Contactor: phase balanceX
Tank type Batch Contactor: phase balance
𝑑 𝐶 𝐴 𝐼 𝑉 𝐼 𝑑𝑡 =− 𝑘 𝑚 𝑎 ( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
𝑑 𝐶 𝐴 𝐼𝐼 𝑉 𝐼𝐼 𝑑𝑡 = 𝑘 𝑚 𝑎 ( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
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16. Tank type Batch Contactor: 𝐶 𝐴 𝐼X
Tank type Batch Contactor: 𝐶 𝐴 𝐼
𝐶 𝐴 𝐼 𝑡 = 𝐶 𝐴,𝑒𝑞 𝐼 − 𝐶 𝐴,𝑒𝑞 𝐼 − 𝐶 𝐴,𝑖 𝐼 𝑒 −𝛽𝑡
𝐶 𝐴,𝑒𝑞 𝐼 =𝑀 𝐶 𝐴,𝑖 𝐼 + 𝐶 𝐴,𝑖 𝐼𝐼 1+𝑀
𝛽= 𝑘 𝑚 𝑎 𝑉 (1+𝑀)
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17. Tank type Batch Contactor: 𝐶 𝐴,𝑒𝑞 𝐼𝐼X
Tank type Batch Contactor: 𝐶 𝐴,𝑒𝑞 𝐼𝐼
𝐶 𝐴,𝑒𝑞 𝐼𝐼 = 𝑉 𝐼 𝐶 𝐴 𝐼 + 𝑉 𝐼𝐼 𝐶 𝐴 𝐼𝐼 𝑀 𝑉 𝐼 + 𝑉 𝐼𝐼
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18. Tank type Batch Contactor: 𝑉 𝐼𝐼X
Tank type Batch Contactor: 𝑉 𝐼𝐼
𝑉 𝐼𝐼 𝑡 = 𝑉 𝑖 𝐼𝐼 − 𝑘 𝑚 𝛼 𝑁 𝐶 𝐴,𝑠𝑎𝑡 𝐼 3 𝜌 𝐼𝐼 t 3
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19. Choose one of the 2 main tubular type mass contactorsX
Choose one of the 2 main tubular type mass contactors
Co-Current
Counter-Current
(Choose One)

20. Counter-Current tubular type mass contactorX
Counter-Current tubular type mass contactor
(Choose a variable)
phase balance
𝑪 𝑨 𝑰
𝑪 𝑨 𝑰𝑰
Back to tubular type list

21. Counter-Current tubular type mass contactor: Phase BalanceX
Counter-Current tubular type mass contactor: Phase Balance
0=− 𝑑 𝑑𝑧 𝑞 𝐼 𝐶 𝐴 𝐼 − 𝑘 𝑚 𝑎 𝑣 𝐴 𝑐 ( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
0= 𝑑 𝑑𝑧 𝑞 𝐼𝐼 𝐶 𝐴 𝐼𝐼 + 𝑘 𝑚 𝑎 𝑣 𝐴 𝑐 ( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
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22. Counter-Current tubular type mass contactor: 𝐶 𝐴 𝐼X
Counter-Current tubular type mass contactor: 𝐶 𝐴 𝐼
𝐶 𝐴 𝐼 𝑧 =𝑀 𝜆 𝐶 𝐴𝐹 𝐼𝐼 − 𝑒 −𝛽𝐿 𝐶 𝐴𝐹 𝐼 𝜆−𝑀 𝑒 𝛽𝐿 +𝜆 𝐶 𝐴𝐹 𝐼 −𝑀 𝐶 𝐴𝐹 𝐼 𝜆−𝑀 𝑒 −𝛽𝐿 𝑒 −𝛽𝑧
𝛽= 𝑘 𝑚 𝑎 𝑞 𝐼𝐼 𝐿 (𝜆−𝑀)
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23. Counter-Current tubular type mass contactor: 𝐶 𝐴 𝐼𝐼X
Counter-Current tubular type mass contactor: 𝐶 𝐴 𝐼𝐼
𝐶 𝐴 𝐼𝐼 = 𝐶 𝐴𝐹 𝐼𝐼 + 𝑞 𝐼 𝑞 𝐼𝐼 (𝐶 𝐴𝐹 𝐼 − 𝐶 𝐴 𝐼 )
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24. Co-Current tubular type mass contactorsX
Co-Current tubular type mass contactors
(Choose a variable)
phase balance
𝑪 𝑨 𝑰
𝑪 𝑨 𝑰𝑰
𝑪 𝑨,𝒆𝒒 𝑰 , 𝑪 𝑨,𝒆𝒒 𝑰𝑰
Back to tubular type list

25. Co-Current tubular type mass contactors: phase balanceX
Co-Current tubular type mass contactors: phase balance
0=− 𝑑 𝑑𝑧 𝑞 𝐼 𝐶 𝐴 𝐼 − 𝑘 𝑚 𝑎 𝑣 𝐴 𝑐 ( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
0=− 𝑑 𝑑𝑧 𝑞 𝐼𝐼 𝐶 𝐴 𝐼𝐼 + 𝑘 𝑚 𝑎 𝑣 𝐴 𝑐 ( 𝐶 𝐴 𝐼 −𝑀 𝐶 𝐴 𝐼𝐼 )
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26. Co-Current tubular type mass contactors: 𝑪 𝑨 𝑰X
Co-Current tubular type mass contactors: 𝑪 𝑨 𝑰
𝐶 𝐴 𝐼 𝑧 = 𝑀 𝑀+𝜆 𝐶 𝐴𝐹 𝐼 +𝜆 C AF II + 𝜆 𝑀+𝜆 𝐶 𝐴𝐹 𝐼 −𝜆 C AF II e −β𝑧
𝛽= 𝑘 𝑚 𝑎 𝑞 𝐼𝐼 𝐿 𝜆+𝑀
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27. Co-Current tubular type mass contactors: 𝑪 𝑨 𝑰𝑰X
Co-Current tubular type mass contactors: 𝑪 𝑨 𝑰𝑰
𝐶 𝐴 𝐼𝐼 𝑧 = 1 𝑀+𝜆 𝐶 𝐴𝐹 𝐼 +𝜆 C AF II + 1 𝑀+𝜆 𝐶 𝐴𝐹 𝐼 −𝜆 C AF II e −β𝑧
𝛽= 𝑘 𝑚 𝑎 𝑞 𝐼𝐼 𝐿 𝜆+𝑀
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28. Co-Current tubular type mass contactors: 𝑪 𝑨,𝒆𝒒 𝑰 , 𝑪 𝑨,𝒆𝒒 𝑰𝑰X
Co-Current tubular type mass contactors: 𝑪 𝑨,𝒆𝒒 𝑰 , 𝑪 𝑨,𝒆𝒒 𝑰𝑰
𝐶 𝐴,𝑒𝑞 𝐼𝐼 = 𝐶 𝐴 𝐼 +𝜆 𝐶 𝐴𝐹 𝐼𝐼 𝜆+𝑀
𝐶 𝐴,𝑒𝑞 𝐼 =𝑀 𝐶 𝐴,𝑒𝑞 𝐼𝐼
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29. Thank you for using the app
By: Ahmed Al-Marjibi